Schwarz et al.: Shifted Hyperbola Revisited - The Two Faces of NMO

In many present-day applications in seismic processing, the assumption of a homogeneous model leads to simple yet powerful approximations, which also work well when heterogeneity is not negligible. While the classical NMO hyperbola assumes an effective constant velocity medium, de Bazelaire, based on optical projections, introduced an alternative way to account for heterogeneity by shifting the reference time rather than the velocity. In this work, we provide new insights into the auxiliary medium concept and introduce a generalized osculating equation, which allows for the forward and inverse transformation between the effective and the optical domain, thereby providing a unified view on currently used stacking approximations. Supported by synthetic tests, we reveal that all higher order operators can be described in and transformed between both domains, which, through combined use, suggests interesting new applications, like, i. e., in diffraction separation or surface-related multiple elimination.

Most current implementations of the CRS operator suffer from the occurrence of conflicting dip situations in the acquired data. To address this properly we apply the idea of the CDS. We use the iCRS operator that can be related to the CRS operator, and show, that conflicting dips can be resolved well in multi-parameter processing. The results are promising and reveal a lot of potential for further applications. This is shown by a diffraction separation technique applied to field data obtained in the Levantine Basin.

Walda et al.: Global Optimization of the CRS Operator Using a Genetic Algorithm

The CRS operator improves the signal to noise ratio significantly due to the consideration of neighboring midpoints as well as the offset. The determination of the required attributes for the CRS operator is often done by the pragmatic approach to get initial values that are refined by a local optimization. This works reasonable for most parts, however in more complex structures like salt bodies the result is not reliable anymore. Additionally the pragmatic approach does not perform particularly well in the presence of conflicting dips. Therefore we propose to use a genetic algorithm based optimization and show that the stack and especially the determined attributes are significantly better.

The imaging of diffracted waves is a crucial challenge in seismic processing, because they carry important information about small-scale subsurface structures. A key step of diffraction imaging is their separation and enhancement in the pre-stack data volume, which requires common-offset processing. However, due to the higher dimensionality of the problem, common-offset stacking is computationally more expensive than the stable and commonly used zero-offset processing. In this work, we motivate a straightforward decomposition principle for diffractions, which establishes a direct connection between zero-offset and common-offset diffraction wavefield attributes based on the decoupling of diffraction raypaths. We show, theoretically and on simple waveform data, that each common-offset diffraction operator can be decomposed exactly into two zero-offset operators. This allows the direct prediction of common-offset diffraction attributes solely based on their zero-offset counterparts. Application of the new method to complex data reveals its ability to reliably image diffractions in the common-offset domain using only results from zero-offset processing as input. The promising results in terms of both image and attributes reveal a high potential for improved pre-stack diffraction separation and diffraction-stereotomography.

Imaging of seismic diffractions is a challenge since it is inherently a 3D problem. Diffractions carry useful information about the subsurface and allow to identify the presence of small-scale heterogeneities and structures e.g. fractures, pinch-outs, thin lenses etc. Thus, diffraction separation and imaging can lead to higher resolution, which is of particular interest for reservoir characterisation and exploration. In this work, we suggest a 3D workflow based on common-reflection-surface (CRS) method for prestack diffraction separation and imaging in time domain. The workflow combines the ideas developed for diffraction separation with the partial CRS stack technique. It comprises not only the diffraction separation facility but also includes a prestack data enhancement, i.e., an improved SNR in diffraction-only data. Application to a 3D synthetic model confirms its effectiveness in prestack diffraction separation. It also demonstrates potential for time migration velocity analysis using diffraction-only data.

3D processing and imaging of diffraction is a challenge in seismic data processing and needs to be focused more. Seismic diffractions carry a lot of information about the subsurface especially in regions with small scale structures e.g. fractures, pinch-outs, thin lenses etc. Thus, diffraction separation and imaging can lead to higher resolution, which is of particular interest for reservoir characterization and exploration. If diffraction-only data are available, they permit to extract information in addition to that obtained from reflection processing. In this work, we suggest a 3D workflow based on common-reflection-surface (CRS) method for prestack diffraction separation and enhancement. Application to a 3D synthetic data set demonstrates advantages compare to poststack diffraction separation. In contrast to poststack diffraction separation, prestack separation workflow makes use of partial CRS which comprises not only the diffraction separation facility but also includes a prestack data enhancement, i.e., an improved SNR in diffraction-only data. It also demonstrates potential for time migration velocity analysis using diffraction-only data.

Remigration trajectories describe the position of an image point in the image domain for different source-receiver offsets as a function of the migration velocity. They can be used for prestack time-migration velocity analysis by means of determining kinematic migration parameters, which in turn, allow to locally correct the velocity model. The main advantage of this technique is that it takes the reflection-point displacement in the midpoint direction into account, thus allowing for a moveout correction for a single reflection point at all offsets of a common image gather (CIG). We have tested the feasibility of the method on synthetic data from three simple models and the Marmousoft data. Our tests show that the proposed tool increases the velocity-model resolution and provides a plausible time-migrated image, even in regions with strong velocity variations. The most effort was spent on the event picking, which is critical to the method.

We present a strategy to time-to-depth conversion and velocity estimation based only on the image-wavefront propagation. It has two main features: (1) it computes the velocity field and the traveltime directly, avoiding the ray-tracing step; and (2) it requires only the knowledge of the image-wavefront at the previous time step. As a consequence, our method tends to be faster than usual techniques and does not carry the constraints and limitations inherent to common ray-tracing strategies. We have tested the feasibility of the method on the original Marmousi velocity model and two smoothed versions of it. Moreover, we migrated the Marmousi data set using the estimated depth velocity models. Our results indicate that the present strategy can be used to construct starting models for velocity-model building in depth migration and/or tomographic methods.

Maciel et al.: Detection of Diffractions on GPR Data Using Support Vector Classifiers

Detection of diffractions is an essential step on diffraction imaging techniques. Due to their smaller amplitudes regarding reflection events, diffraction events are usually treated as noise in standard seismic processing. Diffraction imaging is often used to identify subsurface scattering features with enhanced resolution in comparison to conventional seismic reflection imaging. Several techniques have been presented in literature for separation of diffracted from reflected events. One way is to analyze amplitudes along diffraction time curves in common-offset sections, where it is easier to perceive differences between diffraction and reflection events. Known pattern recognition methods can be used to separate the events. We analyze automatic detection of diffraction points using Support Vector Machines (SVM). We evaluate the ability the method to detect scattering features, using a GPR radargram. Results indicate that pattern recognition methods are a good tool for interpreters when used for detection of diffractions.